knitr::opts_chunk$set(echo = FALSE, warning = FALSE)

This is the supplementary analytic output for the reanalysis of meta-analyses on the effect of music education, carried out for the SUPERAR project


Brief information about the methods used in the analysis:

RMA results with model-based SEs k = number of studies; sqrt in “Variance components” = tau, the standard deviation of true effects; estimate in “Model results” = naive MA estimate

RVE SEs with Satterthwaite small-sample correction Estimate based on a multilevel RE model with constant sampling correlation model (CHE - correlated hierarchical effects - working model) (Pustejovsky & Tipton, 2020; https://osf.io/preprints/metaarxiv/vyfcj/). Interpretation of naive-meta-analysis should be based on these estimates.

Prediction interval Shows the expected range of true effects in similar studies. As an approximation, in 95% of cases the true effect in a new published study can be expected to fall between PI LB and PI UB. Note that these are non-adjusted estimates. An unbiased newly conducted study will more likely fall in an interval centered around bias-adjusted estimate with a wider CI width.

Heterogeneity Tau can be interpreted as the total amount of heterogeneity in the true effects. I^2$ represents the ratio of true heterogeneity to total variance across the observed effect estimates. Estimates calculated by two approaches are reported. This is followed by separate estimates of between- and within-cluster heterogeneity and estimated intra-class correlation of underlying true effects.

Proportion of significant results What proportion of effects were statistically at the alpha level of .05.

ES-precision correlation Kendalls’s correlation between the ES and precision.

4/3PSM Applies a permutation-based, step-function 4-parameter selection model (one-tailed p-value steps = c(.025, .5, 1)). Falls back to 3-parameter selection model if at least one of the three p-value intervals contains less than 5 p-values. For this meta-analysis, we applied 3-parameter selection model by default as there were only 11 independent effects in the opposite direction overall (6%), causing the estimates to be unstable across iterations. pvalue = p-value testing H0 that the effect is zero. ciLB and ciUB are lower and upper bound of the CI. k = number of studies. steps = 3 means that the 4PSM was applied, 2 means that the 3PSM was applied. We also ran two sensitivity analyses of the selection model, the Vevea & Woods (2005) step function model with a priori defined selection weights and the Robust Bayesian Meta-analysis model employing the model-averaging approach (Bartoš & Maier, 2020).

PET-PEESE Estimated effect size of an infinitely precise study. Using 4/3PSM as the conditional estimator instead of PET (can be changed to PET). If the PET-PEESE estimate is in the opposite direction, the effect can be regarded nil. By default (can be changed to PET), the function employs a modified sample-size based estimator (see https://www.jepusto.com/pet-peese-performance/). It also uses the same RVE sandwich-type based estimator in a CHE (correlated hierarchical effects) working model with the identical random effects structure as the primary (naive) meta-analytic model.

We report results for both, PET and PEESE, with the first reported one being the primary (based on the conditional estimator).

WAAP-WLS The combined WAAP-WLS estimator (weighted average of the adequately powered - weighted least squares) tries to identify studies that are adequately powered to detect the meta-analytic effect. If there is less than two such studies, the method falls back to the WLS estimator (Stanley & Doucouliagos, 2015). If there are at least two adequately powered studies, WAAP returns a WLS estimate based on effects from only those studies.

type = 1: WAAP estimate, 2: WLS estimate. kAdequate = number of adequately powered studies

p-uniform P-uniform* is a selection model conceptually similar to p-curve. It makes use of the fact that p-values follow a uniform distribution at the true effect size while it includes also nonsignificant effect sizes. Permutation-based version of p-uniform method, the so-called p-uniform* (van Aert, van Assen, 2021).

p-curve Permutation-based p-curve method. Output should be self-explanatory. For more info see p-curve.com

Power for detecting SESOI and bias-corrected parameter estimates Estimates of the statistical power for detecting a smallest effect sizes of interest equal to .20, .50, and .70 in SD units (Cohen’s d). A sort of a thought experiment, we also assumed that population true values equal the bias-corrected estimates (4/3PSM or PET-PEESE) and computed power for those.

Handling of dependencies in bias-correction methods To handle dependencies among the effects, the 4PSM, p-curve, p-uniform are implemented using a permutation-based procedure, randomly selecting only one focal effect (i.e., excluding those which were not coded as being focal) from a single study and iterating nIterations times. Lastly, the procedure selects the result with the median value of the ES estimate (4PSM, p-uniform) or median z-score of the full p-curve (p-curve).

Results

## $`1`
## $`1`$spatial
## $`1`$spatial$resultsOverall
## $`1`$spatial$resultsOverall$`RMA results with model-based SEs`
## 
## Multivariate Meta-Analysis Model (k = 19; method: REML)
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed            factor 
## sigma^2.1  0.0000  0.0000      8     no           paperID 
## sigma^2.2  0.0481  0.2193     19     no  paperID/effectID 
## 
## Test for Heterogeneity:
## Q(df = 18) = 28.4390, p-val = 0.0557
## 
## Model Results:
## 
## estimate      se    zval    pval    ci.lb   ci.ub    
##   0.2019  0.1264  1.5968  0.1103  -0.0459  0.4497    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## $`1`$spatial$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`
## $`1`$spatial$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$test
##    Coef. Estimate    SE t-stat d.f. (Satt) p-val (Satt) Sig.
##  intrcpt    0.202 0.121   1.67        6.16        0.146     
## 
## $`1`$spatial$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$CIs
##    Coef. Estimate    SE d.f. Lower 95% CI Upper 95% CI
##  intrcpt    0.202 0.121 6.16      -0.0928        0.497
## 
## 
## $`1`$spatial$resultsOverall$`Prediction interval`
## 95% PI LB 95% PI UB 
##    -0.389     0.793 
## 
## $`1`$spatial$resultsOverall$Heterogeneity
##                           Tau                           I^2 
##                     0.2193068                    25.5078742 
##                 Jackson's I^2 Between-cluster heterogeneity 
##                    52.3300000                     0.0000000 
##  Within-cluster heterogeneity                           ICC 
##                    25.5100000                     0.0000000 
## 
## $`1`$spatial$resultsOverall$`Proportion of significant results`
## [1] 0.05263158
## 
## $`1`$spatial$resultsOverall$`Publication bias`
## [1] "Publication bias corrections not carried out"
## 
## 
## $`1`$spatial$resultsTable
##                k       g [95% CI]  95% PI [LB, UB]               SE 
##               19 0.2 [-0.09, 0.5]  [-0.389, 0.793]             0.12 
##              Tau              I^2 
##             0.22              26% 
## 
## 
## $`1`$processingSpeed
## $`1`$processingSpeed$resultsOverall
## $`1`$processingSpeed$resultsOverall$`RMA results with model-based SEs`
## 
## Multivariate Meta-Analysis Model (k = 22; method: REML)
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed            factor 
## sigma^2.1  0.0272  0.1650      8     no           paperID 
## sigma^2.2  0.0854  0.2922     22     no  paperID/effectID 
## 
## Test for Heterogeneity:
## Q(df = 21) = 57.4626, p-val < .0001
## 
## Model Results:
## 
## estimate      se    zval    pval    ci.lb   ci.ub    
##   0.1726  0.1271  1.3576  0.1746  -0.0766  0.4217    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## $`1`$processingSpeed$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`
## $`1`$processingSpeed$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$test
##    Coef. Estimate    SE t-stat d.f. (Satt) p-val (Satt) Sig.
##  intrcpt    0.173 0.128   1.35        6.68        0.221     
## 
## $`1`$processingSpeed$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$CIs
##    Coef. Estimate    SE d.f. Lower 95% CI Upper 95% CI
##  intrcpt    0.173 0.128 6.68       -0.133        0.478
## 
## 
## $`1`$processingSpeed$resultsOverall$`Prediction interval`
## 95% PI LB 95% PI UB 
##    -0.676     1.021 
## 
## $`1`$processingSpeed$resultsOverall$Heterogeneity
##                           Tau                           I^2 
##                     0.3355215                    66.0278236 
##                 Jackson's I^2 Between-cluster heterogeneity 
##                    90.2500000                    15.9600000 
##  Within-cluster heterogeneity                           ICC 
##                    50.0600000                     0.2400000 
## 
## $`1`$processingSpeed$resultsOverall$`Proportion of significant results`
## [1] 0.2272727
## 
## $`1`$processingSpeed$resultsOverall$`Publication bias`
## [1] "Publication bias corrections not carried out"
## 
## 
## $`1`$processingSpeed$resultsTable
##                  k         g [95% CI]    95% PI [LB, UB]                 SE 
##                 22 0.17 [-0.13, 0.48]    [-0.676, 1.021]               0.13 
##                Tau                I^2 
##               0.34                66% 
## 
## 
## $`1`$phonolProcessing
## $`1`$phonolProcessing$resultsOverall
## $`1`$phonolProcessing$resultsOverall$`RMA results with model-based SEs`
## 
## Multivariate Meta-Analysis Model (k = 39; method: REML)
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed            factor 
## sigma^2.1  0.0000  0.0000     15     no           paperID 
## sigma^2.2  0.0468  0.2163     39     no  paperID/effectID 
## 
## Test for Heterogeneity:
## Q(df = 38) = 63.5002, p-val = 0.0059
## 
## Model Results:
## 
## estimate      se    zval    pval    ci.lb   ci.ub    
##   0.1368  0.0814  1.6802  0.0929  -0.0228  0.2963  . 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## $`1`$phonolProcessing$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`
## $`1`$phonolProcessing$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$test
##    Coef. Estimate     SE t-stat d.f. (Satt) p-val (Satt) Sig.
##  intrcpt    0.137 0.0677   2.02        7.76       0.0792    .
## 
## $`1`$phonolProcessing$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$CIs
##    Coef. Estimate     SE d.f. Lower 95% CI Upper 95% CI
##  intrcpt    0.137 0.0677 7.76      -0.0203        0.294
## 
## 
## $`1`$phonolProcessing$resultsOverall$`Prediction interval`
## 95% PI LB 95% PI UB 
##    -0.349     0.623 
## 
## $`1`$phonolProcessing$resultsOverall$Heterogeneity
##                           Tau                           I^2 
##                     0.2162839                    34.2520660 
##                 Jackson's I^2 Between-cluster heterogeneity 
##                    24.0200000                     0.0000000 
##  Within-cluster heterogeneity                           ICC 
##                    34.2500000                     0.0000000 
## 
## $`1`$phonolProcessing$resultsOverall$`Proportion of significant results`
## [1] 0.1025641
## 
## $`1`$phonolProcessing$resultsOverall$`Publication bias`
## [1] "Publication bias corrections not carried out"
## 
## 
## $`1`$phonolProcessing$resultsTable
##                  k         g [95% CI]    95% PI [LB, UB]                 SE 
##                 39 0.14 [-0.02, 0.29]    [-0.349, 0.623]               0.07 
##                Tau                I^2 
##               0.22                34% 
## 
## 
## $`1`$memory
## $`1`$memory$resultsOverall
## $`1`$memory$resultsOverall$`RMA results with model-based SEs`
## 
## Multivariate Meta-Analysis Model (k = 57; method: REML)
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed            factor 
## sigma^2.1  0.0133  0.1155     19     no           paperID 
## sigma^2.2  0.0448  0.2116     57     no  paperID/effectID 
## 
## Test for Heterogeneity:
## Q(df = 56) = 111.3234, p-val < .0001
## 
## Model Results:
## 
## estimate      se    zval    pval   ci.lb   ci.ub      
##   0.2531  0.0734  3.4471  0.0006  0.1092  0.3970  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## $`1`$memory$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`
## $`1`$memory$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$test
##    Coef. Estimate     SE t-stat d.f. (Satt) p-val (Satt) Sig.
##  intrcpt    0.253 0.0746   3.39        13.4      0.00466   **
## 
## $`1`$memory$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$CIs
##    Coef. Estimate     SE d.f. Lower 95% CI Upper 95% CI
##  intrcpt    0.253 0.0746 13.4       0.0923        0.414
## 
## 
## $`1`$memory$resultsOverall$`Prediction interval`
## 95% PI LB 95% PI UB 
##    -0.276     0.782 
## 
## $`1`$memory$resultsOverall$Heterogeneity
##                           Tau                           I^2 
##                     0.2410852                    54.7441424 
##                 Jackson's I^2 Between-cluster heterogeneity 
##                    87.2200000                    12.5600000 
##  Within-cluster heterogeneity                           ICC 
##                    42.1900000                     0.2300000 
## 
## $`1`$memory$resultsOverall$`Proportion of significant results`
## [1] 0.1754386
## 
## $`1`$memory$resultsOverall$`Publication bias`
## [1] "Publication bias corrections not carried out"
## 
## 
## $`1`$memory$resultsTable
##                 k        g [95% CI]   95% PI [LB, UB]                SE 
##                57 0.25 [0.09, 0.41]   [-0.276, 0.782]              0.07 
##               Tau               I^2 
##              0.24               55% 
## 
## 
## $`1`$math
## $`1`$math$resultsOverall
## $`1`$math$resultsOverall$`RMA results with model-based SEs`
## 
## Multivariate Meta-Analysis Model (k = 18; method: REML)
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed            factor 
## sigma^2.1  0.0351  0.1872      9     no           paperID 
## sigma^2.2  0.0000  0.0000     18     no  paperID/effectID 
## 
## Test for Heterogeneity:
## Q(df = 17) = 17.9298, p-val = 0.3933
## 
## Model Results:
## 
## estimate      se    zval    pval    ci.lb   ci.ub    
##   0.1940  0.0995  1.9493  0.0513  -0.0011  0.3891  . 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## $`1`$math$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`
## $`1`$math$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$test
##    Coef. Estimate    SE t-stat d.f. (Satt) p-val (Satt) Sig.
##  intrcpt    0.194 0.102    1.9        6.09        0.105     
## 
## $`1`$math$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$CIs
##    Coef. Estimate    SE d.f. Lower 95% CI Upper 95% CI
##  intrcpt    0.194 0.102 6.09      -0.0545        0.443
## 
## 
## $`1`$math$resultsOverall$`Prediction interval`
## 95% PI LB 95% PI UB 
##    -0.293     0.681 
## 
## $`1`$math$resultsOverall$Heterogeneity
##                           Tau                           I^2 
##                     0.1872316                    44.4943199 
##                 Jackson's I^2 Between-cluster heterogeneity 
##                    75.9200000                    44.4900000 
##  Within-cluster heterogeneity                           ICC 
##                     0.0000000                     1.0000000 
## 
## $`1`$math$resultsOverall$`Proportion of significant results`
## [1] 0.1111111
## 
## $`1`$math$resultsOverall$`Publication bias`
## [1] "Publication bias corrections not carried out"
## 
## 
## $`1`$math$resultsTable
##                  k         g [95% CI]    95% PI [LB, UB]                 SE 
##                 18 0.19 [-0.05, 0.44]    [-0.293, 0.681]                0.1 
##                Tau                I^2 
##               0.19                44% 
## 
## 
## $`1`$literacy
## $`1`$literacy$resultsOverall
## $`1`$literacy$resultsOverall$`RMA results with model-based SEs`
## 
## Multivariate Meta-Analysis Model (k = 50; method: REML)
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed            factor 
## sigma^2.1  0.0000  0.0000     23     no           paperID 
## sigma^2.2  0.0000  0.0000     50     no  paperID/effectID 
## 
## Test for Heterogeneity:
## Q(df = 49) = 42.8907, p-val = 0.7179
## 
## Model Results:
## 
## estimate      se    zval    pval    ci.lb   ci.ub    
##   0.0600  0.0445  1.3484  0.1775  -0.0272  0.1472    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## $`1`$literacy$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`
## $`1`$literacy$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$test
##    Coef. Estimate     SE t-stat d.f. (Satt) p-val (Satt) Sig.
##  intrcpt     0.06 0.0411   1.46        5.68        0.197     
## 
## $`1`$literacy$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$CIs
##    Coef. Estimate     SE d.f. Lower 95% CI Upper 95% CI
##  intrcpt     0.06 0.0411 5.68      -0.0419        0.162
## 
## 
## $`1`$literacy$resultsOverall$`Prediction interval`
## 95% PI LB 95% PI UB 
##     -0.02      0.14 
## 
## $`1`$literacy$resultsOverall$Heterogeneity
##                           Tau                           I^2 
##                  5.245164e-06                  3.909034e-08 
##                 Jackson's I^2 Between-cluster heterogeneity 
##                  0.000000e+00                  0.000000e+00 
##  Within-cluster heterogeneity                           ICC 
##                  0.000000e+00                  8.800000e-01 
## 
## $`1`$literacy$resultsOverall$`Proportion of significant results`
## [1] 0.04
## 
## $`1`$literacy$resultsOverall$`Publication bias`
## [1] "Publication bias corrections not carried out"
## 
## 
## $`1`$literacy$resultsTable
##                  k         g [95% CI]    95% PI [LB, UB]                 SE 
##                 50 0.06 [-0.04, 0.16]      [-0.02, 0.14]               0.04 
##                Tau                I^2 
##                  0                 0% 
## 
## 
## $`1`$intelligence
## $`1`$intelligence$resultsOverall
## $`1`$intelligence$resultsOverall$`RMA results with model-based SEs`
## 
## Multivariate Meta-Analysis Model (k = 32; method: REML)
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed            factor 
## sigma^2.1  0.0000  0.0000     16     no           paperID 
## sigma^2.2  0.0171  0.1309     32     no  paperID/effectID 
## 
## Test for Heterogeneity:
## Q(df = 31) = 36.1729, p-val = 0.2397
## 
## Model Results:
## 
## estimate      se    zval    pval    ci.lb   ci.ub    
##   0.1133  0.0735  1.5409  0.1233  -0.0308  0.2574    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## $`1`$intelligence$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`
## $`1`$intelligence$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$test
##    Coef. Estimate     SE t-stat d.f. (Satt) p-val (Satt) Sig.
##  intrcpt    0.113 0.0669   1.69        7.52        0.131     
## 
## $`1`$intelligence$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$CIs
##    Coef. Estimate     SE d.f. Lower 95% CI Upper 95% CI
##  intrcpt    0.113 0.0669 7.52      -0.0427        0.269
## 
## 
## $`1`$intelligence$resultsOverall$`Prediction interval`
## 95% PI LB 95% PI UB 
##    -0.197     0.423 
## 
## $`1`$intelligence$resultsOverall$Heterogeneity
##                           Tau                           I^2 
##                     0.1308709                    18.6747020 
##                 Jackson's I^2 Between-cluster heterogeneity 
##                    64.5900000                     0.0000000 
##  Within-cluster heterogeneity                           ICC 
##                    18.6700000                     0.0000000 
## 
## $`1`$intelligence$resultsOverall$`Proportion of significant results`
## [1] 0.09375
## 
## $`1`$intelligence$resultsOverall$`Publication bias`
## [1] "Publication bias corrections not carried out"
## 
## 
## $`1`$intelligence$resultsTable
##                  k         g [95% CI]    95% PI [LB, UB]                 SE 
##                 32 0.11 [-0.04, 0.27]    [-0.197, 0.423]               0.07 
##                Tau                I^2 
##               0.13                19% 
## 
## 
## $`1`$inhibition
## $`1`$inhibition$resultsOverall
## $`1`$inhibition$resultsOverall$`RMA results with model-based SEs`
## 
## Multivariate Meta-Analysis Model (k = 17; method: REML)
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed            factor 
## sigma^2.1  0.0000  0.0000      7     no           paperID 
## sigma^2.2  0.0528  0.2297     17     no  paperID/effectID 
## 
## Test for Heterogeneity:
## Q(df = 16) = 32.9813, p-val = 0.0074
## 
## Model Results:
## 
## estimate      se    zval    pval    ci.lb   ci.ub    
##   0.0557  0.1120  0.4969  0.6193  -0.1639  0.2752    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## $`1`$inhibition$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`
## $`1`$inhibition$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$test
##    Coef. Estimate     SE t-stat d.f. (Satt) p-val (Satt) Sig.
##  intrcpt   0.0557 0.0764  0.728        3.68         0.51     
## 
## $`1`$inhibition$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$CIs
##    Coef. Estimate     SE d.f. Lower 95% CI Upper 95% CI
##  intrcpt   0.0557 0.0764 3.68       -0.164        0.275
## 
## 
## $`1`$inhibition$resultsOverall$`Prediction interval`
## 95% PI LB 95% PI UB 
##    -0.535     0.647 
## 
## $`1`$inhibition$resultsOverall$Heterogeneity
##                           Tau                           I^2 
##                     0.2297003                    42.0317851 
##                 Jackson's I^2 Between-cluster heterogeneity 
##                    37.4200000                     0.0000000 
##  Within-cluster heterogeneity                           ICC 
##                    42.0300000                     0.0000000 
## 
## $`1`$inhibition$resultsOverall$`Proportion of significant results`
## [1] 0.1176471
## 
## $`1`$inhibition$resultsOverall$`Publication bias`
## [1] "Publication bias corrections not carried out"
## 
## 
## $`1`$inhibition$resultsTable
##                  k         g [95% CI]    95% PI [LB, UB]                 SE 
##                 17 0.06 [-0.16, 0.28]    [-0.535, 0.647]               0.08 
##                Tau                I^2 
##               0.23                42% 
## 
## 
## 
## $`2`
## $`2`$phonologicalAwareness
## $`2`$phonologicalAwareness$resultsOverall
## $`2`$phonologicalAwareness$resultsOverall$`RMA results with model-based SEs`
## 
## Multivariate Meta-Analysis Model (k = 18; method: REML)
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed            factor 
## sigma^2.1  0.0000  0.0000     11     no           paperID 
## sigma^2.2  0.0699  0.2643     18     no  paperID/effectID 
## 
## Test for Heterogeneity:
## Q(df = 17) = 36.1512, p-val = 0.0044
## 
## Model Results:
## 
## estimate      se    zval    pval   ci.lb   ci.ub    
##   0.2177  0.1015  2.1447  0.0320  0.0187  0.4166  * 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## $`2`$phonologicalAwareness$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`
## $`2`$phonologicalAwareness$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$test
##    Coef. Estimate     SE t-stat d.f. (Satt) p-val (Satt) Sig.
##  intrcpt    0.218 0.0934   2.33        8.27       0.0472    *
## 
## $`2`$phonologicalAwareness$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$CIs
##    Coef. Estimate     SE d.f. Lower 95% CI Upper 95% CI
##  intrcpt    0.218 0.0934 8.27      0.00344        0.432
## 
## 
## $`2`$phonologicalAwareness$resultsOverall$`Prediction interval`
## 95% PI LB 95% PI UB 
##    -0.405     0.840 
## 
## $`2`$phonologicalAwareness$resultsOverall$Heterogeneity
##                           Tau                           I^2 
##                     0.2643395                    51.8018030 
##                 Jackson's I^2 Between-cluster heterogeneity 
##                    54.7300000                     0.0000000 
##  Within-cluster heterogeneity                           ICC 
##                    51.8000000                     0.0000000 
## 
## $`2`$phonologicalAwareness$resultsOverall$`Proportion of significant results`
## [1] 0.1111111
## 
## $`2`$phonologicalAwareness$resultsOverall$`Publication bias`
## [1] "Publication bias corrections not carried out"
## 
## 
## $`2`$phonologicalAwareness$resultsTable
##               k      g [95% CI] 95% PI [LB, UB]              SE             Tau 
##              18  0.22 [0, 0.43]  [-0.405, 0.84]            0.09            0.26 
##             I^2 
##             52% 
## 
## 
## $`2`$readingFLuency
## $`2`$readingFLuency$resultsOverall
## $`2`$readingFLuency$resultsOverall$`RMA results with model-based SEs`
## 
## Multivariate Meta-Analysis Model (k = 5; method: REML)
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed            factor 
## sigma^2.1  0.0000  0.0000      5     no           paperID 
## sigma^2.2  0.0000  0.0000      5     no  paperID/effectID 
## 
## Test for Heterogeneity:
## Q(df = 4) = 6.2812, p-val = 0.1791
## 
## Model Results:
## 
## estimate      se    zval    pval    ci.lb   ci.ub    
##   0.1579  0.0966  1.6338  0.1023  -0.0315  0.3473    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## $`2`$readingFLuency$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`
## $`2`$readingFLuency$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$test
##    Coef. Estimate     SE t-stat d.f. (Satt) p-val (Satt) Sig.
##  intrcpt    0.158 0.0772   2.05        1.99        0.178     
## 
## $`2`$readingFLuency$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$CIs
##    Coef. Estimate     SE d.f. Lower 95% CI Upper 95% CI
##  intrcpt    0.158 0.0772 1.99       -0.176        0.492
## 
## 
## $`2`$readingFLuency$resultsOverall$`Prediction interval`
## 95% PI LB 95% PI UB 
##    -0.056     0.371 
## 
## $`2`$readingFLuency$resultsOverall$Heterogeneity
##                           Tau                           I^2 
##                  4.629868e-06                  3.576893e-08 
##                 Jackson's I^2 Between-cluster heterogeneity 
##                  0.000000e+00                  0.000000e+00 
##  Within-cluster heterogeneity                           ICC 
##                  0.000000e+00                  5.000000e-01 
## 
## $`2`$readingFLuency$resultsOverall$`Proportion of significant results`
## [1] 0.2
## 
## $`2`$readingFLuency$resultsOverall$`Publication bias`
## [1] "Publication bias corrections not carried out"
## 
## 
## $`2`$readingFLuency$resultsTable
##                  k         g [95% CI]    95% PI [LB, UB]                 SE 
##                  5 0.16 [-0.18, 0.49]    [-0.056, 0.371]               0.08 
##                Tau                I^2 
##                  0                 0% 
## 
## 
## 
## $`3`
## $`3`$executiveFunctions
## $`3`$executiveFunctions$resultsOverall
## $`3`$executiveFunctions$resultsOverall$`RMA results with model-based SEs`
## 
## Multivariate Meta-Analysis Model (k = 24; method: REML)
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed            factor 
## sigma^2.1  0.0000  0.0000      7     no           paperID 
## sigma^2.2  0.1645  0.4055     24     no  paperID/effectID 
## 
## Test for Heterogeneity:
## Q(df = 23) = 96.4425, p-val < .0001
## 
## Model Results:
## 
## estimate      se    zval    pval   ci.lb   ci.ub      
##   0.5118  0.1309  3.9085  <.0001  0.2552  0.7685  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## $`3`$executiveFunctions$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`
## $`3`$executiveFunctions$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$test
##    Coef. Estimate     SE t-stat d.f. (Satt) p-val (Satt) Sig.
##  intrcpt    0.512 0.0958   5.34        4.64      0.00386   **
## 
## $`3`$executiveFunctions$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$CIs
##    Coef. Estimate     SE d.f. Lower 95% CI Upper 95% CI
##  intrcpt    0.512 0.0958 4.64         0.26        0.764
## 
## 
## $`3`$executiveFunctions$resultsOverall$`Prediction interval`
## 95% PI LB 95% PI UB 
##    -0.506     1.529 
## 
## $`3`$executiveFunctions$resultsOverall$Heterogeneity
##                           Tau                           I^2 
##                      0.405533                     64.699082 
##                 Jackson's I^2 Between-cluster heterogeneity 
##                     63.460000                      0.000000 
##  Within-cluster heterogeneity                           ICC 
##                     64.700000                      0.000000 
## 
## $`3`$executiveFunctions$resultsOverall$`Proportion of significant results`
## [1] 0.5
## 
## $`3`$executiveFunctions$resultsOverall$`Publication bias`
## [1] "Publication bias corrections not carried out"
## 
## 
## $`3`$executiveFunctions$resultsTable
##                 k        g [95% CI]   95% PI [LB, UB]                SE 
##                24 0.51 [0.26, 0.76]   [-0.506, 1.529]               0.1 
##               Tau               I^2 
##              0.41               65% 
## 
## 
## 
## $`4`
## $`4`$aggressiveBehavior
## $`4`$aggressiveBehavior$resultsOverall
## $`4`$aggressiveBehavior$resultsOverall$`RMA results with model-based SEs`
## 
## Multivariate Meta-Analysis Model (k = 7; method: REML)
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed            factor 
## sigma^2.1  1.6671  1.2911      4     no           paperID 
## sigma^2.2  0.0000  0.0000      7     no  paperID/effectID 
## 
## Test for Heterogeneity:
## Q(df = 6) = 77.7832, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb   ci.ub    
##  -1.2086  0.6760  -1.7878  0.0738  -2.5336  0.1164  . 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## $`4`$aggressiveBehavior$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`
## $`4`$aggressiveBehavior$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$test
##    Coef. Estimate   SE t-stat d.f. (Satt) p-val (Satt) Sig.
##  intrcpt    -1.21 0.68  -1.78        2.99        0.174     
## 
## $`4`$aggressiveBehavior$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$CIs
##    Coef. Estimate   SE d.f. Lower 95% CI Upper 95% CI
##  intrcpt    -1.21 0.68 2.99        -3.38         0.96
## 
## 
## $`4`$aggressiveBehavior$resultsOverall$`Prediction interval`
## 95% PI LB 95% PI UB 
##    -5.846     3.429 
## 
## $`4`$aggressiveBehavior$resultsOverall$Heterogeneity
##                           Tau                           I^2 
##                      1.291144                     99.290049 
##                 Jackson's I^2 Between-cluster heterogeneity 
##                     99.780000                     99.290000 
##  Within-cluster heterogeneity                           ICC 
##                      0.000000                      1.000000 
## 
## $`4`$aggressiveBehavior$resultsOverall$`Proportion of significant results`
## [1] 0.4285714
## 
## $`4`$aggressiveBehavior$resultsOverall$`Publication bias`
## [1] "Publication bias corrections not carried out"
## 
## 
## $`4`$aggressiveBehavior$resultsTable
##                   k          g [95% CI]     95% PI [LB, UB]                  SE 
##                   7 -1.21 [-3.38, 0.96]     [-5.846, 3.429]                0.68 
##                 Tau                 I^2 
##                1.29                 99% 
## 
## 
## $`4`$hyperactivityImpulsivity
## $`4`$hyperactivityImpulsivity$resultsOverall
## $`4`$hyperactivityImpulsivity$resultsOverall$`RMA results with model-based SEs`
## 
## Multivariate Meta-Analysis Model (k = 7; method: REML)
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed            factor 
## sigma^2.1  0.0000  0.0000      3     no           paperID 
## sigma^2.2  1.2423  1.1146      7     no  paperID/effectID 
## 
## Test for Heterogeneity:
## Q(df = 6) = 60.4069, p-val < .0001
## 
## Model Results:
## 
## estimate      se    zval    pval    ci.lb   ci.ub    
##   0.0089  0.5003  0.0178  0.9858  -0.9717  0.9895    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## $`4`$hyperactivityImpulsivity$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`
## $`4`$hyperactivityImpulsivity$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$test
##    Coef. Estimate    SE t-stat d.f. (Satt) p-val (Satt) Sig.
##  intrcpt  0.00889 0.263 0.0339         1.7        0.977     
## 
## $`4`$hyperactivityImpulsivity$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$CIs
##    Coef. Estimate    SE d.f. Lower 95% CI Upper 95% CI
##  intrcpt  0.00889 0.263  1.7        -1.34         1.36
## 
## 
## $`4`$hyperactivityImpulsivity$resultsOverall$`Prediction interval`
## 95% PI LB 95% PI UB 
##    -4.929     4.947 
## 
## $`4`$hyperactivityImpulsivity$resultsOverall$Heterogeneity
##                           Tau                           I^2 
##                      1.114597                     90.604306 
##                 Jackson's I^2 Between-cluster heterogeneity 
##                     91.840000                      0.000000 
##  Within-cluster heterogeneity                           ICC 
##                     90.600000                      0.000000 
## 
## $`4`$hyperactivityImpulsivity$resultsOverall$`Proportion of significant results`
## [1] 0.5714286
## 
## $`4`$hyperactivityImpulsivity$resultsOverall$`Publication bias`
## [1] "Publication bias corrections not carried out"
## 
## 
## $`4`$hyperactivityImpulsivity$resultsTable
##                  k         g [95% CI]    95% PI [LB, UB]                 SE 
##                  7 0.01 [-1.34, 1.36]    [-4.929, 4.947]               0.26 
##                Tau                I^2 
##               1.11                91% 
## 
## 
## $`4`$`self-control`
## $`4`$`self-control`$resultsOverall
## $`4`$`self-control`$resultsOverall$`RMA results with model-based SEs`
## 
## Multivariate Meta-Analysis Model (k = 4; method: REML)
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed            factor 
## sigma^2.1  1.4959  1.2231      3     no           paperID 
## sigma^2.2  0.0004  0.0203      4     no  paperID/effectID 
## 
## Test for Heterogeneity:
## Q(df = 3) = 86.4838, p-val < .0001
## 
## Model Results:
## 
## estimate      se    zval    pval    ci.lb   ci.ub    
##   0.8654  0.7147  1.2109  0.2259  -0.5354  2.2661    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## $`4`$`self-control`$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`
## $`4`$`self-control`$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$test
##    Coef. Estimate    SE t-stat d.f. (Satt) p-val (Satt) Sig.
##  intrcpt    0.865 0.713   1.21           2        0.349     
## 
## $`4`$`self-control`$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$CIs
##    Coef. Estimate    SE d.f. Lower 95% CI Upper 95% CI
##  intrcpt    0.865 0.713    2        -2.21         3.94
## 
## 
## $`4`$`self-control`$resultsOverall$`Prediction interval`
## 95% PI LB 95% PI UB 
##    -5.230     6.961 
## 
## $`4`$`self-control`$resultsOverall$Heterogeneity
##                           Tau                           I^2 
##                      1.223253                     99.693947 
##                 Jackson's I^2 Between-cluster heterogeneity 
##                     99.840000                     99.670000 
##  Within-cluster heterogeneity                           ICC 
##                      0.030000                      1.000000 
## 
## $`4`$`self-control`$resultsOverall$`Proportion of significant results`
## [1] 0.5
## 
## $`4`$`self-control`$resultsOverall$`Publication bias`
## [1] "Publication bias corrections not carried out"
## 
## 
## $`4`$`self-control`$resultsTable
##                  k         g [95% CI]    95% PI [LB, UB]                 SE 
##                  4 0.87 [-2.21, 3.94]     [-5.23, 6.961]               0.71 
##                Tau                I^2 
##               1.22               100% 
## 
## 
## $`4`$prosocialBehavior
## $`4`$prosocialBehavior$resultsOverall
## $`4`$prosocialBehavior$resultsOverall$`RMA results with model-based SEs`
## 
## Multivariate Meta-Analysis Model (k = 4; method: REML)
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed            factor 
## sigma^2.1  0.0000  0.0000      3     no           paperID 
## sigma^2.2  0.0021  0.0454      4     no  paperID/effectID 
## 
## Test for Heterogeneity:
## Q(df = 3) = 4.8858, p-val = 0.1804
## 
## Model Results:
## 
## estimate      se    zval    pval    ci.lb   ci.ub    
##   0.0285  0.0472  0.6039  0.5459  -0.0640  0.1210    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## $`4`$prosocialBehavior$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`
## $`4`$prosocialBehavior$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$test
##    Coef. Estimate     SE t-stat d.f. (Satt) p-val (Satt) Sig.
##  intrcpt   0.0285 0.0288  0.991         1.1        0.491     
## 
## $`4`$prosocialBehavior$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$CIs
##    Coef. Estimate     SE d.f. Lower 95% CI Upper 95% CI
##  intrcpt   0.0285 0.0288  1.1       -0.269        0.326
## 
## 
## $`4`$prosocialBehavior$resultsOverall$`Prediction interval`
## 95% PI LB 95% PI UB 
##    -0.180     0.237 
## 
## $`4`$prosocialBehavior$resultsOverall$Heterogeneity
##                           Tau                           I^2 
##                    0.04538964                   28.89708215 
##                 Jackson's I^2 Between-cluster heterogeneity 
##                   36.00000000                    0.00000000 
##  Within-cluster heterogeneity                           ICC 
##                   28.90000000                    0.00000000 
## 
## $`4`$prosocialBehavior$resultsOverall$`Proportion of significant results`
## [1] NA
## 
## $`4`$prosocialBehavior$resultsOverall$`Publication bias`
## [1] "Publication bias corrections not carried out"
## 
## 
## $`4`$prosocialBehavior$resultsTable
##                  k         g [95% CI]    95% PI [LB, UB]                 SE 
##                  4 0.03 [-0.27, 0.33]     [-0.18, 0.237]               0.03 
##                Tau                I^2 
##               0.05                29% 
## 
## 
## $`4`$aggressionPropensity
## $`4`$aggressionPropensity$resultsOverall
## $`4`$aggressionPropensity$resultsOverall$`RMA results with model-based SEs`
## 
## Multivariate Meta-Analysis Model (k = 2; method: REML)
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed            factor 
## sigma^2.1  0.0017  0.0409      2     no           paperID 
## sigma^2.2  0.0017  0.0409      2     no  paperID/effectID 
## 
## Test for Heterogeneity:
## Q(df = 1) = 1.0804, p-val = 0.2986
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb   ci.ub    
##  -0.0267  0.0688  -0.3883  0.6978  -0.1616  0.1082    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## $`4`$aggressionPropensity$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`
## $`4`$aggressionPropensity$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$test
##    Coef. Estimate     SE t-stat d.f. (Satt) p-val (Satt) Sig.
##  intrcpt  -0.0267 0.0688 -0.388           1        0.764     
## 
## $`4`$aggressionPropensity$resultsOverall$`RVE SEs with Satterthwaite small-sample correction`$CIs
##    Coef. Estimate     SE d.f. Lower 95% CI Upper 95% CI
##  intrcpt  -0.0267 0.0688    1       -0.901        0.848
## 
## 
## $`4`$aggressionPropensity$resultsOverall$`Prediction interval`
## 95% PI LB 95% PI UB 
##    -0.865     0.811 
## 
## $`4`$aggressionPropensity$resultsOverall$Heterogeneity
##                           Tau                           I^2 
##                    0.05788512                    7.44597151 
##                 Jackson's I^2 Between-cluster heterogeneity 
##                   65.53000000                    3.72000000 
##  Within-cluster heterogeneity                           ICC 
##                    3.72000000                    0.50000000 
## 
## $`4`$aggressionPropensity$resultsOverall$`Proportion of significant results`
## [1] NA
## 
## $`4`$aggressionPropensity$resultsOverall$`Publication bias`
## [1] "Publication bias corrections not carried out"
## 
## 
## $`4`$aggressionPropensity$resultsTable
##                  k         g [95% CI]    95% PI [LB, UB]                 SE 
##                  2 -0.03 [-0.9, 0.85]    [-0.865, 0.811]               0.07 
##                Tau                I^2 
##               0.06                 7%

Forest plots

Funnel plots